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1 AN ABSTRACT OF THE THESIS OF Jeremy H Donaldson for the degree of Master of Science in Civil Engineering presented on September 13, Title: A Kinetic Model for Dissolved Gas Transport in the Presence of Trapped Gas. Abstract approved: Redacted for Privacy Jonathan D. Istok Understanding the processes involved in the transport of dissolved gas plumes in groundwater aquifers is essential for comprehending the effect that these transport processes can have on site characterization and remedial design applications. Previous laboratory and field studies have indicated that dissolved gas transport in groundwater can be greatly affected by the presence of even small amounts of trapped gas in the pore space of an aquifer. Recently, Fry et al. (1995) reported an increase in retardation factors R (where R = pore water velocity/dissolved gas velocity) for dissolved oxygen with increasing amounts of trapped gas. Fry showed that the retardation factor for a dissolved gas can be predicted using a relationship between the dimensionless Henry's Law constant for the dissolved gas, the volumetric gas content (i.e., the fraction of the total volume occupied by trapped gas), and the volumetric water content (i.e., the fraction of total volume occupied by water). In their experiments, Fry et al. (1995) found this relationship in an equilibrium model accurately predicted observed retardation factors for dissolved oxygen when the volumetric gas content was small, but underpredicted retardation factors for larger volumetric gas contents. Also, predicted breakthrough curves for dissolved oxygen obtained by incorporating this relationship into the advection-dispersion equation did not match the shape of experimentally observed breakthrough curves. The experimental curves were asymmetrical with long tails indicating that the local equilibrium assumption is inaccurate and suggesting that mass transfer of oxygen between the aqueous and trapped gas phases is diffusion limited.

2 In an effort to gain further understanding of this process, a kinetic model was developed for dissolved gas transport that includes a diffusion type expression for the rate of gas transfer between the mobile aqueous and trapped gas phases. The model was tested in a series of transport experiments conducted in sand packed columns with varying amounts and composition of trapped gas. The kinetic model was found to better fit the shape of dissolved oxygen breakthrough and elution curves than the equilibrium model of Fry et al. (1995). This model was then extended to the case of two-dimensions to simulate dissolved gas transport in the presence of trapped gas under conditions that approximate injection and extraction wells used to distribute dissolved gases in an aquifer (e.g. to promote in situ bioremediation processes or to perform a dissolved gas tracer test). We then compared these predicted concentrations with measured concentrations obtained in a series of dissolved gas transport experiments in a large-scale physical aquifer model using two dissolved gases (oxygen and hydrogen) with very different physical properties. The model could accurately fit the development and movement of these plumes providing that key parameters, the amount of trapped gas and the effective mass transfer coefficient, were adjusted between the injection and drift stages.

3 A Kinetic Model for Dissolved Gas Transport in the Presence of Trapped Gas by Jeremy H. Donaldson A THESIS submitted to Oregon State University In partial fulfillment of the requirements for the degree of Master of Science Completed September 13, 1996 Commencement June, 1997

4 Master of Science thesis of Jeremy H. Donaldson presented September 13, 1996 APPROVED: Redacted for Privacy Major Prbfessor. representing Civil Engineering Redacted for Privacy Chair of epartment of Civil, Construction, and Environmental Engineering Redacted for Privacy Dean of Gradu,atk School I understand that my thesis will become part of the permanent collection of Oregon State University Libraries. My signature below authorizes release of my thesis to any reader upon request. Redacted for Privacy Jeremy H. Donaldson, Author

5 ACKNOWLEDGMENTS First, thanks to my major professor, Dr. Jonathan Istok, for the guidance and encouragement that allowed me to finally finish the "never ending thesis." I was honored when Jack took me on as a student, and am honored to have had the opportunity to work with him for so long. I'll be dropping his name for years. Thanks to Dr. John Selker and Dr. Lew Semprini for teaching me so much over the last few years, for serving on my committee, and for taking such delight in terrorizing me about the questions in my oral exam. I guess that's the price you pay for being friendly with your professors, but it's worth it. Thanks to Dr. Virginia Fry for doing the work that laid the foundation for this thesis. And for laughing at all of my jokes. All of them. Even the really bad ones. Thanks to my family for the encouragement and support when I decided to go back to school and throughout the entire process. Finally, and most importantly, thanks to my wife Kathy. Without her, none of this would have been possible. Even if it had been possible, it would have been miserable. Thanks for being the most important person in my life.

6 CONTRIBUTION OF AUTHORS Dr. Jonathan Istok was an integral part of all phases of this project, and is a coauthor of chapters 2 and 3. Kirk O'Reilly and Don Mohr provided editing and feedback for chapters 2 and 3, with Don Mohr providing particular insight on the discussion in Mark Humphrey and Chris Hawelka assisted in editing chapter 2.

7 TABLE OF CONTENTS Page 1 INTRODUCTION 1 2. DEVELOPMENT AND LABORATORY TESTING OF A KINETIC MODEL FOR DISSOLVED OXYGEN PARTITIONING AND TRANSPORT IN POROUS MEDIA IN THE PRESENCE OF TRAPPED GAS Abstract Introduction Objectives Model Development Materials and Methods Overview Sand Properties Column Preparation Transport Experiments Parameter Estimation Results and Discussion Kinetic Model Performance Effect of Trapped Gas on P Effect of Trapped Gas on R Effect of Trapped Gas on co Summary and Conclusions Acknowledgments References DISSOLVED GAS TRANSPORT IN THE PRESENCE OF A TRAPPED GAS PHASE: EXPERIMENTAL VALIDATION OF A 2-DIMENSIONAL KINETIC MODEL 40

8 TABLE OF CONTENTS (CONTINUED) 3.1 Abstract 3.2 Introduction 3.3 Objectives 3.4 Model Development 3.5 Materials and Methods Overview Physical Aquifer Model Porous Media Transport Experiments Sampling and Analysis Methods Numerical Simulations Results and Discussion Page Transport Experiments Injection stage Drift stage Numerical Simulations Bromide Oxygen Hydrogen Sensitivity Analyses Effect of varying a' Effect of varying Og Summary Acknowledgments References 4.0 SUMMARY BIBLIOGRAPHY 77

9 LIST OF FIGURES Figure Page 2.1 (a) Conceptual model for dissolved gas transport in presence of trapped gas phase (b) Control volume used in development of dissolved gas transport model 2.2 Definition of concentrations used to compute mass transfer of dissolved gas from trapped gas phase to mobile aqueous phase Laboratory column apparatus used in dissolved gas transport experiments Example bromide and dissolved oxygen breakthrough and elution curves (experiment 2). 2.5 (a) Example elution curves fro bromide (experiments 2 and 3) (b) Example breakthrough curves for dissolved oxygen (experiments 2 and 3) 2.6 Effect of trapped gas volume on fitted valued of (a) Peclet number, P (b) retardation factor, R and (c) dimensionless parameter, w (a)conceptual model and (b)control volume Isometric view of PAM Plan view of sandpack showing locations of sand pack boundaries and injection and extraction wells and the coordinate system used in numerical modeling Observed and predicted aqueous phase concentrations for (a)bromide, (b)oxygen, and (c)hydrogen Observed and predicted drift stage centerline aqueous phase concentrations for (a)bromide, (b)oxygen, and (c)hydrogen 3.6 Effect of (a)effective mass transfer coefficient and (b)amount of trapped gas on initial spreading of oxygen plume. 3.7 Effect of (a)effective mass transfer coefficient and (b)amount of trapped gas on oxygen plume during drift stage at 20 and 69 hours 3.8 Effect of effective mass transfer coefficient on separation of dissolved gas and trapped gas plumes during drift stage at 44 hours

10 LIST OF TABLES Table Page 2.1 Properties of selected gasses at 101 kpa Summary of experimental conditions and fitted model parameters Summary of experimental conditions and model parameters. 51

11 For Kathy

12 A Kinetic Model for Dissolved Gas Transport in the Presence of Trapped Gas 1. INTRODUCTION Understanding the processes involved in the transport of dissolved gas plumes in groundwater aquifers is essential for grasping the effect that these gases can have on site characterization and remedial design applications. Dissolved gases are frequently used as either electron donors (e.g. oxygen or methane) or electron acceptors (e.g. hydrogen) in microbially mitigated bioremediation schemes (Chiang et al., 1989; Semprini et al., 1992), and the availability of these gases can affect the rates of contaminant breakdown. Also, dissolved gases can serve as reaction products and intermediates, and the rates of these processes can be affected by dissolved gas transport. (Lovely et al., 1994). Selected dissolved gases (e.g. helium, sulfur hexafluoride) are also frequently used as groundwater tracers because they are non reactive, have higher diffusion coefficients (allowing them to penetrate into smaller pores) and lower detection limits (allowing their use at lower concentrations) than anions such as Cl- or Br- or organic dyes (Wilson and Mackay, 1993) Previous laboratory and field studies have indicated that dissolved gas transport in groundwater can be greatly affected by the presence of even small amounts of trapped gas in the pore space (the term 'trapped gas' is used here instead of previously used terms e.g., 'residual air' or 'encapsulated air' to emphasize that the gas phase can be of arbitrary composition). For example, Carter et al (1959) reported retardation factors R (where R = pore water velocity/dissolved gas velocity) for dissolved helium as large as 16 during transport in an unconfined aquifer which they attributed to the combined effects of partitioning of helium into trapped air below the water table and the volatilization of helium from groundwater into the unsaturated zone. In column experiments. Gupta et al. (1994) reported retardation factors for dissolved helium of 1 in completely water saturated porous media, but as large as 3 when small amounts of trapped air were present in the pore space. In another series of column experiments, Fry et al. (1995) reported an increase in retardation factors for dissolved oxygen with increasing amounts of trapped gas and found that the retardation factor, R for a dissolved gas could be reasonably

13 2 predicted using a relationship between the dimensionless Henry's Law constant for the dissolved gas, the volumetric gas content (i.e., the fraction of the total volume occupied by trapped gas), and the volumetric water content (i.e., the fraction of total volume occupied by water). The use of this relationship implied that dissolved gas concentrations in the two phases was in equilibrium, which is analogous to the 'local equilibrium' assumption frequently used to describe processes of sorption, ion exchange, etc. for other solutes. In the experiments of Fry et al. (1995) this relationship accurately predicted observed retardation factors for dissolved oxygen when the volumetric gas content was small, but underpredicted retardation factors for larger volumetric gas contents. Also, predicted breakthrough curves for dissolved oxygen obtained by incorporating this relationship into the advection-dispersion equation did not match the shape of experimentally observed breakthrough curves. The experimental curves were asymmetrical with long tails indicating that the local equilibrium assumption is inaccurate and suggesting that mass transfer of oxygen between the aqueous and trapped gas phases is diffusion limited. The overall objective of Chapter 2 was to gain further understanding of the process of dissolved gas transport and partitioning in the presence of a trapped gas in an otherwise water saturated porous media. To do this we developed a kinetic model for dissolved gas transport that includes a diffusion type expression for the rate of gas transfer between the mobile aqueous and trapped gas phases. The model was tested in a series of transport experiments conducted in sand packed columns that were prepared to contain varying amounts and composition of trapped gas. The kinetic model was found to better fit the shape of dissolved oxygen breakthrough and elution curves than the equilibrium model of Fry et al. (1995). The primary objective of chapter 3 was to gain further understanding of dissolved gas transport in the presence of trapped gas in an otherwise water saturated porous media under conditions that approximate those that apply when injection and extraction wells are used to distribute dissolved gases in an aquifer (e.g. to promote in situ bioremediation processes or to perform a dissolved gas tracer test). To do this we extended the onedimensional kinetic model of chapter 2 to the case of two-dimensional flow and transport

14 3 of a dissolved gas. We then compared these predicted concentrations with measured concentrations obtained in a series of dissolved gas transport experiments in a large-scale physical aquifer model using two dissolved gases (oxygen and hydrogen) with very different physical properties.

15 4 2. DEVELOPMENT AND LABORATORY TESTING OF A KINETIC MODEL FOR DISSOLVED OXYGEN PARTITIONING AND TRANSPORT IN POROUS MEDIA IN THE PRESENCE OF TRAPPED GAS J.H. Donaldson, *J.D. Istok, and M.D. Humphrey Department of Civil Engineering Oregon State University Corvallis, OR K.T. O'Reilly, C.A. Hawelka, and D.H. Mohr Chevron Research and Technology Company 100 Chevron Way Richmond, CA *Corresponding author Technical Paper for Ground Water September 25, 1996

16 5 2.1 Abstract The ability to predict the transport of dissolved gases in the presence of small amounts of trapped gas in an otherwise water saturated porous medium is needed for a variety of applications. However, an existing model based on equilibrium partitioning of dissolved gas between aqueous and trapped gas phases does not accurately predict the shape of experimentally observed breakthrough and elution curves in column experiments. The objective of this study was to develop and test a kinetic model for dissolved gas transport that combines the advection-dispersion equation with diffusion controlled mass transfer of dissolved gas between the aqueous and trapped gas phases. The model assumes one-dimensional, steady-state groundwater flow, a single dissolved gas component, and a stationary trapped gas phase with constant volume. The model contains three independent parameters: the Pec let number, P, retardation factor, R, and dimensionless mass transfer parameter, w. The model can be well fit to the shape of breakthrough and elution curves for dissolved oxygen in column experiments performed with a poorly graded sand and varying amount and composition of trapped gas. Estimated values of P for the bromide tracer increased from 5.92 to 174, corresponding to a decrease in dispersivity from 5.02 to 0.17 cm, as the trapped gas volume increased from 0 to 30 % of the pore space. It is speculated that this effect is due to a narrower pore size distribution (and hence more uniform pore scale velocity distribution) caused by trapped gas bubbles selectively occupying the largest pores. Estimated values of R increased from 1 to 13.6 as the trapped gas volume increased and confirmed earlier observations that even small amounts of trapped gas can significantly reduce rates of dissolved gas transport. Estimated values of w ranged from 0.3 to Although it was not possible to independently measure mass transfer coefficients or interfacial areas. values computed from flowrates and estimated w values are consistent with values computed by assuming (1) that interfacial area is proportional to trapped gas volume, (2) that trapped gas bubbles are spheres with diameters the same size as soil particles, and (3) that mass transfer is limited by diffusion of dissolved oxygen through water films surrounding trapped gas bubbles.

17 6 2.2 Introduction The ability to predict the transport of dissolved gases in groundwater aquifers is needed for a variety of applications. For example, in situ bioremediation, the use of indigenous microorganisms to degrade contaminants in groundwater, has generated much interest in recent years. Many indigenous microorganisms are aerobic and utilize oxygen as an electron acceptor (Chiang et al., 1989), while others can utilize hydrogen or methane (Semprini et al., 1992). The stoichiometric demand for these gases can be large, and in a large contaminant spill all the dissolved gas within the plume can be consumed before the contaminant is degraded. With this in mind, various methods for increasing dissolved gas concentrations have been proposed including the injection of gas enriched water (Roberts et al., 1990; Semprini et al., 1992) and direct gas injection (Pankow et al., 1993). To a large degree, the success of these techniques depends on the rate of transport and degree of mixing of introduced dissolved gases with the contaminated groundwater. Conversely, anaerobic respiration processes typically generate gaseous products such as nitrogen, hydrogen sulfide, and methane and the rates of these processes can also be affected by dissolved gas transport (Lovely et al., 1994). Information on dissolved gas transport is also needed to interpret the results of dissolved gas tracer tests performed to determine groundwater velocity, or the aquifer porosity and dispersivity in site characterization studies. In this application, water containing a known concentration of a dissolved gas (e.g., helium, neon, or sulfur hexafluoride) is injected into an aquifer and concentrations of the dissolved gas are measured in groundwater samples collected from downgradient monitoring wells. Dissolved gases are desirable for this purpose because (1) certain inert gases (e.g., He) can be considered chemically nonreactive in groundwater, thus permitting their use as conservative tracers, (2) dissolved gases typically have large diffusion coefficients which allow them to readily penetrate into small pores, and (3) many dissolved gases have lower

18 7 detection limits (allowing their use at lower concentrations) than many other solutes frequently used as tracers (e.g., anions such as bromide or chloride) (Wilson and Mackay, 1993). Although dissolved gas transport plays an important role in the design of in situ bioremediation systems and the interpretation of dissolved gas tracer tests, only limited research has been performed on the transport characteristics of dissolved gases in porous media. For this reason, the relative magnitude of various dissolved gas transport processes are poorly understood. Early experiments comparing the transport of chloride and dissolved helium in laboratory columns and in the field were performed by Carter et al. (1959). Carter reported retardation factors R (where R = pore water velocity/dissolved gas velocity) for helium that ranged from 1.17 to as high as 16 (the pore water velocity was determined from the breakthrough curve for chloride). Carter attributed the higher retardation factors for helium observed in columns and a confined aquifer to the diffusion of the smaller, neutral helium molecules into small pores that the larger, charged chloride ions could not enter. The higher values of R observed in an unconfined aquifer were attributed to the volatilization of helium from the water table. Gupta et al. (1994) also compared the rates of dissolved helium and chloride transport in laboratory columns and in the field and reported retardation factors for dissolved helium of 1.0 for completely water saturated porous media, but as large as 3.0 when small amounts of trapped air were present in the pore space. Gupta et al. attributed the higher retardation factors in the presence of trapped gas to mass transfer of helium from the aqueous phase to the trapped gas phase. Most recently Fry et al. (1995), in a series of transport experiments in packed laboratory columns, showed that the presence of small amounts of trapped air in the pore space of an otherwise water saturated sand could result in retardation factors for dissolved oxygen ranging from 1.0 to 8.0. Fry et al. (1995) proposed the following equation to predict the retardation factor, R for a dissolved gas: R = 1 + HCq (1)

19 8 where H is the dimensionless Henry's Law constant for the dissolved gas, Og is the volumetric gas content (i.e., the fraction of the total volume occupied by trapped gas), and 9aq is the volumetric water content (i.e., the fraction of total volume occupied by water). Fry et al. (1995) speculated that the large value of H for many gases of environmental interest (e.g., H = 28 for dissolved oxygen at 15 C) suggests that the transport of these gases in groundwater systems will be substantially retarded by the presence of even small amounts of trapped gas in the pore space. Equation 1 predicted retardation factors well for oxygen when Og/Oaq was small, but underpredicted retardation factors for larger values of OgiOaq. Fry et al. (1995) suggested that the short residence times used in the column experiments (4 to 6 minutes) might have been too small to allow equilibrium to develop between dissolved oxygen concentrations in the trapped gas and aqueous phases. Also, the equilibrium model did not fit the shape of the tails of the breakthrough and elution curves well. The curves were asymmetrical with long tails suggesting that mass transfer of oxygen between the aqueous and trapped gas phases was diffusion limited. 2.3 Objectives The overall objective of this study was to gain further understanding of the process of dissolved gas transport and partitioning in the presence of a trapped gas in an otherwise water saturated porous media. In particular, we sought to evaluate a kinetic model for dissolved gas transport that includes a rate term for gas transfer between the mobile aqueous and trapped gas phases. The model was tested using data obtained in a series of transport experiments conducted in sand packed columns prepared to contain varying amounts and composition of trapped gas. It is hoped that the developed model and parameters reported here will be useful for obtaining preliminary estimates of rates of dissolved gas transport under field situations.

20 9 2.4 Model Development Our conceptual model for dissolved gas transport in the presence of small amounts of trapped gas in an otherwise water saturated porous media considers the trapped gas phase to exist as small bubbles of various sizes, dispersed throughout the pore space (Figure 2.1a). The term 'trapped gas' is used here instead of previously used terms (e.g., 'residual air' or 'encapsulated air') to emphasize that the gas phase is assumed stationary and can be of arbitrary composition. The pore space also contains a mobile aqueous phase. In general, several dissolved gas components may be present in both the aqueous and trapped gas phases and these may include gases found in air (e.g., nitrogen, oxygen, or carbon dioxide), gases introduced to promote in situ bioremediation (e.g., oxygen, methane, or hydrogen), or gases introduced during dissolved gas tracer tests (e.g., helium, neon, or sulfur hexafluoride). For simplicity, we will consider only the case of a single dissolved gas component here, although the extension of these concepts to the simultaneous transport and partitioning of several dissolved gases is relatively straightforward. The control volume is taken to be large relative to the size of individual pores and assumed to consist of a stationary gas phase with volume Vg, a mobile aqueous phase with volume Vag, and a stationary solid phase which is assumed to contain no gas (Figure 2.1b). The volume of pore space Vpores = 4V = Vg + Vag where (I) is the porosity and V is the total volume. Volumetric fluid contents can also be defined for each phase: Og = Vg/V, Oaq = Vag/V, with 08 + eaci = 0. The total gas phase pressure, volume, and temperature are assumed to be constant. During transport, dissolved gas can transfer between the trapped gas and mobile aqueous phases by diffusion. The direction and rate of mass transfer is controlled by the gradient in chemical potential between the two phases; at equilibrium the chemical potentials for all components in both phases are equal. Assuming dissolved gas concentrations in the aqueous phase are small, the condition for equilibrium can be written in terms of gas concentrations in the two phases

21 a) 0 (1) 0 c 10 F- Ha, cn 0 tn al 0 u) 0 a_ a) -0 0 a) a) 0 -C 1: Cr) 2 Figure 2.1 (a) Conceptual model for dissolved gas transport in presence of trapped gas (b) Control volume used in development of dissolved gas transport model.

22 11 using Henry's Law Cg = HCaq (2) where Cg is the dissolved gas concentration in the trapped gas phase and Caq is the dissolved gas concentration in the mobile aqueous phase. When trapped gas is present in the pore space, a gas-liquid interface exists at the edges of trapped gas bubbles (Figure 2.2). The rate of interphase mass transfer can be predicted using an analysis based on film theory (e.g., Cuss ler, 1994, p ). In that analysis, the mass transfer rate is controlled by the rate of diffusion of the solute across a thin layer assumed to exist at the phase interface. Referring to Figure 2.2, the mass flux, mg, of a dissolved gas from the interior of a trapped gas bubble to the phase interface can be written mg = kg(cg Cg,o) (3) where kg is the gas phase mass transfer coefficient and Cg,o is the gas concentration in the trapped gas phase at the interface. Similarly, the mass flux from the interface to the interior of the aqueous phase, ma can be written maq = kaq(caq.o Caq) (4) where kaq is the aqueous phase mass transfer coefficient and Cap is the gas concentration in the mobile aqueous phase at the interface. The mass transfer coefficient for each phase is proportional to the diffusivity of the dissolved gas in that phase (Cuss ler, 1994). Because gas phase diffusivities are typically several orders of magnitude larger than aqueous phase diffusivities (e.g., see Table 2.1), kaq is usually much smaller than kg and interphase mass transfer will be controlled by the rate of mass transfer from the bulk aqueous phase to the interface. Equilibrium, as described by Henry's Law, is assumed to exist at the interface between the two phases i.e., C2,0= HCaq.o. Combining this result with the condition that mg = ma (no accumulation or depletion of mass at the interface), gives an expression for the flux across the interface,

23 trapped. mobile aqueous gas phase. phase Cg.. '.. aq, o.... :flux. C aq K... g,o CI..... Figure 2.2. Definition of concentrations used to compute mass transfer of dissolved gas from trapped gas phase to mobile aqueous phase.

24 H Cr Molecular weight 'Solubility in water 2Diffusivity in oxygen, Dg 3Dimensionless Henry's law 4Diffusivity in water, Dag Gas constant, H (g/mol) (mg/i.) (cm2/s) (cm2/s) Air (273 K) x 10-5 Oxygen x 10-5 Nitrogen (273 K) x 10-5 Helium (298 K) x 10-5 'Measured at T = 288 K (Colt, 1984) 2Cussler (1994) 3Measured at T = 273 K (Fry et al., 1995) 4Measured at T = 298 K (Cussler, 1994) Cr)

25 14 m = a(hcaq Cg) (5) where a is an overall mass transfer coefficient given by a 1 1 H (6) 17g Equations 5 and 6 can be combined with a statement of conservation of mass for dissolved gas in the trapped gas phase (Figure 2.2) to obtain an expression for the rate of change of mass in the trapped gas phase due to interphase mass transfer ( Aga0 0 == ) ( HCaq Cg) (7) g at v where t is time, Ag is the interfacial area between the trapped gas and aqueous phases (i.e. the combined surface area of all trapped gas bubbles), and V is total volume. If the gas phase concentration, Cg is smaller than the gas phase concentration in equilibrium with the aqueous phase, HC aq, ac at > 0 and the direction of mass transfer will be from the aqueous phase to the trapped gas phase. Differential equations describing aqueous phase transport of a dissolved gas can be obtained by combining a statement of conservation of mass for the control volume in Figure 2.1b with the well known advection dispersion equation (e.g. Bear, 1972). For the case of steady-state one-dimensional flow of the aqueous phase we can write ac aca ac g--g+e ge D "q O aq at aq aq aq ax ax' v (8) where D is the dispersion coefficient, D = 6vaq, 6 is the dispersivity of the porous media, vaq is the average aqueous phase velocity, vaq = q/oaq, where q is the aqueous phase flux, and x is position. It is hypothesized that equations 7 and 8 describe the aqueous phase transport of a dissolved gas in the presence of a trapped gas phase in an otherwise water saturated porous media. In the next section we will test this hypothesis by comparing model predictions with the results of experiments performed in small laboratory columns. For a

26 15 column with length L and total volume V, the aqueous phase flux q becomes, q = QLN, where Q is the total flow rate through the column and L/V is the column cross-sectional area (measured perpendicular to the flow direction). In the transport experiments, the initial conditions will be pinitial C aq(x, t = k/i %-'aq (9a) and where Caq Cg(x, t initial initial 0) = Cg = HCaq (9b) initial and Cg are the initial concentrations in the aqueous and gas phases and will be assumed uniform along the column length. The boundary condition at the column inlet will be a constant flux boundary condition of the form ( ac, + v = V C (10a) aq aq aq x=0 where Ca is the specified concentration of the dissolved gas in the column feed solution. The boundary condition at the outlet end of the column is aca L, t) 0 (10b) axg(x Equation 10b is a form of the so-called 'Danckwerts' boundary condition (Pearson, 1959) that has been shown to be an accurate outlet boundary condition for use with the advection-dispersion equation to describe the results of laboratory column experiments (van Genuchten, 1981). Analytical solutions are obtained more easily by writing equations 7 and 8 in terms of the following dimensionless variables: vaqt T = L LOqt (11a) (11b)

27 16 P V aql V aql L D vaqo 5 (11c) e R= 1 + (11d) Oaq a Ag Q (11e) where T is a dimensionless number that describes the ratio of cumulative water pumped through the column to the volume of water the column contains and is typically referred to as 'pore volumes', P is the column Peclet number (the ratio of advective to dispersive transport processes; see e.g., Bear, 1972), R is the retardation factor for the dissolved gas, and co is a dimensionless parameter that includes the product of the mass transfer coefficient and interfacial area. Dimensionless dissolved gas concentrations in the mobile aqueous and trapped gas phases can be defined as C aq Laq (12a) aq Co L-aq C C g H(Ca q aq caingitial) (12b) With these definitions, equations 7 and 8 can be written acg at = CO (Caq (13) 2C aca ac 1 a aca atq + (R 1)--1 = aq (14) at P ax2 ax and equations 9 and 10 can be written

28 17 Cg(X, T = 0) = 0 Caq(X, T = 0) = 0 _ acaq + c 171 ax aq) X = 0 1 (16a) acaq ax (X= 1, T) = o (16b) It should be noted that similar equations have been proposed to describe the analogous case of solute transport with diffusion limited sorption/desorption (e.g., Lindstrom and Boersma, 1973). In that case, the rate of solute mass transfer from the mobile aqueous phase to the stationary solid phase is limited by the rate of diffusion through a thin film of stagnant water assumed to cover solid surfaces. At equilibrium, solute concentrations in the aqueous and solid phases are related by a partition coefficient that is unique for each solute. In our case, the rate of mass transfer of a dissolved gas from the mobile aqueous phase to the stationary trapped gas phase is limited by the rate of diffusion through a thin film of stagnant water assumed to exist at the outer surface of trapped gas bubbles. At equilibrium, dissolved gas concentrations in the aqueous and gas phases are related by a Henry's Law constant that is unique for each dissolved gas.

29 Materials and Methods Overview The ability of the kinetic model to predict dissolved gas transport in the presence of trapped gas was tested in a series of experiments conducted in small laboratory columns (5.8 cm inside diameter by 25 cm long). In each experiment a sand-packed column was first saturated with water and then partially drained and refilled to trap gas in the pore space; the total volume and composition of the trapped gas were varied from one experiment to the next. Then water containing a known concentration of bromide and dissolved oxygen was pumped through the column in a pulse-type injection test. These solutes were used because the results of previous experiments (data not shown) indicated that, for the soil used in these experiments, bromide acted as a conservative tracer and that significant chemical and biological utilization of dissolved oxygen does not occur within the time period of these experiments. Dissolved oxygen and bromide concentrations were measured on samples of column effluent collected during the experiment and were used to develop breakthrough and elution curves for each solute. Estimates for model parameters P, R, and co were obtained by fitting these curves to an analytical solution to equations 13 to 16 using a least-squares procedure. Evaluation of model performance was made by comparing predicted and observed breakthrough and elution curves Sand Properties The sand used in the column experiments is classified taxonomically in the Winchester series of a mixed, mesic Xeric Torripsamments and was collected from a site in Hermiston, OR from a depth between 1 and 2 meters. The total carbon content, determined by combustion in a Dohrmann carbon analyzer, is 0.11%. The sand was

30 19 passed through a 4.75 mm sieve before packing and had a median grain diameter of 0.8 mm, a uniformity coefficient of 2.9, and is classified as a poorly graded sand (ASTM, 1985). The particle density of the sand, determined by helium pycnometry, is 2.83 g/cm Column Preparation Four sets of three transport experiments were performed. The first experiment in each set was performed using a fully water saturated column packed underwater to avoid trapping air in the pore space. The column was packed while held in a vertical position; approximately ten equal-volume aliquots of air dry soil were allowed to settle through the water and then consolidated by manual tamping with a metal rod. After the last aliquot was consolidated, the column was sealed and removed from the water bath. To further ensure the absence of trapped gas approximately 5 L of de-gassed water (prepared by vigorously stirring tap water under a vacuum) was pumped through the column to dissolve any remaining air bubbles. The absence of trapped air bubbles in the sand pack was confirmed by visual inspection using a hand lens. This packing method resulted in a bulk density of 1.75 g/cm3 and a porosity, (I). of The weight of the water saturated column was measured prior to the start of the first experiment in each set. The remainder of the experiments were performed with a known amount and composition of trapped gas (Table 2.2). To entrap gas, the columns were held vertically and allowed to drain with the column inlet connected to gas (either air, nitrogen, or helium) at atmospheric pressure. The column was then refilled with gas saturated water (prepared by bubbling air, nitrogen, or helium in tap water). The initial volume of trapped gas was determined by subtracting the weight of the refilled column from the water saturated column weight and dividing the weight difference by the density of water. The volume of trapped gas was varied between experiments in each set by varying the time allowed for drainage, but it was not possible to obtain identical trapped gas volumes for all experiments by this method. The vertical distribution of trapped gas was not entirely uniform; generally the largest amounts of trapped gas were observed in

31 Experiment Trapped Q g Oaq Og/Oaq vaq P S.E. 8 R S.E. a) S.E. aa g I Ag la number gas (mi./ (cm3/ (cm3/ min) cm3) cm3) (cm/s) (cm) (cm3/s) (cm2) (cm/s) 1 air air x air x air air x air I x o-3 7 N x N x N x Ile x Ile x Ile x 10-4 I Computed using Og and assumption that trapped gas bubbles are spherical with diameter = 0.8 mm. S.E. = Standard Error

32 21 the upper portion of the column, but a quantitative description of the trapped gas distribution could not be obtained. However, the results of several additional experiments (including some in which the flow direction within the column was reversed) and numerical simulations not presented here indicated that small variations in the spatial distribution of trapped gas bubbles along the column length are not important for predicting dissolved gas concentrations in the column effluent. The columns were also weighed to determine trapped gas volume periodically during each experiment. In all cases, the volume of trapped gas was observed to increase during the breakthrough portion of transport experiments (described below) and decrease during the elution portion. The values of Og/Oaq in Table 2.2 represent the average trapped gas volume for each experiment Transport Experiments Transport experiments were conducted in a constant temperature (15 0C) room. Test solutions were prepared in two 10 L carboys (Figure 2.3). One carboy contained air saturated water, prepared by bubbling air through tap water; the other contained oxygen saturated water with 100 mg/l Br prepared by bubbling oxygen through tap water into which had been dissolved a known amount of KBr. The dissolved oxygen concentration in the air saturated water ranged between 9.8 and 10.2 mg/l, while the dissolved oxygen concentration in the oxygen saturated water ranged between 47 and 49 mg/l. The two carboys were connected by 3.8 mm ID copper tubing to a two-way valve leading to a pump. Copper tubing was used throughout the system to minimize oxygen diffusion through the tubing walls. In the first three experiments (1-3) the flow rate, Q was 2 ml/min (giving aqueous phase velocities, vaq between and cm/s); in the remaining experiments (4-12) the flow rate was 10 ml/min (vaq between and cm/s). The column outlet was connected in series to two flow-through cells. The flowthrough cells were made of cylindrical pieces of solid acrylic plastic, 5.2 cm diameter x 7.6 cm length, with a 0.87 cm diameter hole drilled down the long axis of each piece.

33 Sand packed column Bromide electrode Thermocouple To waste Flow through cells Oxygen probe 17,04kump Ion specific o o meter (=:), 00 1:3 o o Dissolved oxygen meter Compressed air it /441,717Ifilr, Compressed oxygen Datalogger.f.r T,44 Omg/L Br />/v/z/z/ 100mg/L Br To microcomputer

34 23 The first cell was used to measure Br concentrations and contained a combination glass body bromide electrode (Cole-Parmer Instrument Company, Niles, Illinois). The bromide electrode was connected to an ion-specific meter (Accumet Model 25, Denver Instrument Company, Arvada, Colorado) which displayed the probe potential in millivolts. Potential measurements were converted to concentrations using standard curves developed prior to the start of each experiment. Standard curves were linear and had coefficients of determination exceeding 0.99 for all experiments. The second cell was used to measure dissolved oxygen concentration and contained a Clark-type polarigraphic oxygen probe (Model 5331, Yellow Springs Instrument Co., Yellow Springs, Ohio), which entered from the bottom of the cell, halfway along the length. The oxygen probe was connected to a dissolved oxygen meter (Model 5300, Yellow Springs Instrument Co.) which displayed the dissolved oxygen concentration as a percent of the dissolved oxygen concentration in a air-saturated tap water calibration solution. The bromide and dissolved oxygen probes were connected to a datalogger (Model 21X, Campbell Scientific, Logan, Utah) which recorded the measurements and displayed the results on a microcomputer. Measurements were collected at approximately one minute intervals so that several hundred measured concentrations for both solutes were obtained in each experiment. In some experiments, manual water sampling and analysis with bench-top ion specific electrodes and dissolved oxygen probes were made to confirm measured concentrations obtained with the flowthrough cells. Transport experiments were conducted by first pumping air saturated water into the column to establish steady-state flow conditions. The breakthrough phase of each experiment was started by switching the column feed to the carboy containing the oxygen saturated water/bromide solution. Bromide and dissolved oxygen concentrations in the column effluent were measured continuously until concentrations of both solutes were identical to those in the carboy. The elution phase was started by switching the column feed to the carboy containing the air saturated water. During elution, bromide and dissolved oxygen concentrations were measured until effluent bromide concentration was zero and effluent dissolved oxygen concentration was identical to that in the carboy.

35 24 Oxygen was used as the dissolved gas in these experiments because it is easily detected and because of the importance of dissolved oxygen transport to the design of many in situ bioremediation treatment technologies. It should be noted that in our columns, oxygen behaved conservatively, i.e., no reduction in dissolved oxygen concentrations occurred due to chemical or microbiological processes. This was confirmed by mass balance calculations on column feed and effluent concentrations Parameter Estimation Values of the three dimensionless parameters: the Peclet number, P, the retardation factor, R, and the dimensionless mass transfer parameter, co, were estimated using the computer program CFITM (van Genuchten, 1981). For each experiment, the breakthrough and elution curves for the bromide tracer were first used to obtain an estimate for P, assuming R = 1 and w = 0. The dispersivity, 6, was computed from the Peclet number using equation 11c. Then, the breakthrough and elution curves for dissolved oxygen were fit to obtain estimates for R and w using the estimated value for P obtained from the bromide data. An estimate of the standard error was also obtained for each parameter for each experiment. 2.6 Results and Discussion Kinetic Model Performance In general, the kinetic model provided an accurate description of bromide and dissolved oxygen breakthrough and elution curves. For example, Figure 2.4 shows the results for experiment 2 where the flow rate was 2 ml/min, the trapped gas was air, and the trapped gas volume, 0g/ea,i was 0.06 (Table 2.2). The broken line fit to the bromide

36 1.2 o Bromide observed -- Bromide fit Dissolved oxygen observed Dissolved oxygen equilibrium model fit "o Dissolved oxygen kinetic model fit CD fa. 0 a 0 oca a cr a <>" 0.2 srm PORE VOLUMES

37 26 data is for the case R = I and co 0. The estimated Pec let number = 25.0 and the computed dispersivity S = 1.2 cm. The broken line fit to the dissolved oxygen data is for the advection-dispersion equation with the equilibrium mass transfer model of Fry et al. (1995) (equation 1) with R = The equilibrium model matched the observed data poorly especially on the tails of the curves. The solid line in Figure 2.4 shows the kinetic model fit with P = 25.0, R = 3.28, and 0) = Predicted concentrations closely matched measured concentrations even along the asymmetrical tails of the breakthrough and elution curves. The fitted values of retardation factor for the equilibrium and kinetic models are the same and thus both models give the same predicted location for the centroid of the breakthrough curve. However, the kinetic model more accurately predicted the tails of the breakthrough and elution curves. Results for other experiments were similar; the kinetic model consistently provided a more complete description of dissolved oxygen transport than the equilibrium model. A summary of fitted model parameters is in Table 2.2. Standard errors (not shown) for parameter estimates were relatively small, generally less than 10 % of the estimated values Effect of Trapped Gas on P Estimated values of the Peclet number, P, increased and computed values of dispersivity decreased with increasing volume of trapped gas. Example bromide elution curves for experiments 2 and 3 illustrate this trend (Figure 2.5a). In experiment 2, where Og/Oaq = 0.06, the fitted Peclet number was 25.0 and the computed dispersivity was 1.20 cm. In experiment 3, where Og/Oaq = 0.14, the fitted Peclet number was 47.6 and the computed dispersivity was 0.63 cm. In general, computed dispersivities for all experiments were fairly small, less than 5.07 cm, which is typical for uniform sands in column experiments (Bear, 1972). The observed variations in Peclet number and dispersivity with trapped gas content were supported by the results of other experiments (Table 2.2); in general estimated values of P increased approximately linearly with

38 27 N 0 co (f) ct N 0 0 ci 0 boo Figure 2.5. (a) Example elution curves for bromide (experiments 2 and 3) (b) Example breakthrough curves for dissolved oxygen (experiments 2 and 3).

39 Experiment 2 R = 3.28 co = 2.36, 0.8 eg = Icy PORE VOLUMES

40 29 increasing 0g/0aq (Figure 2.6a). One possible explanation is that the presence of trapped gas narrows the effective pore size distribution in the sandpack. This could occur because trapped gas would act as a nonwetting fluid, selectively occupying the larger pores (e.g., Bear, 1972). A more uniform distribution of pore sizes would create a more uniform distribution in pore scale velocity and a decreased dispersivity. The only exception to this trend occurred in experiments 10, 11, and 12, when helium was the trapped gas and the fitted values of P remained essentially constant for all values of 0g/0aq (Figure 2.6a). Since the properties of helium differ greatly from the properties of the other gases used in these experiments (Table 2.1) it is speculated that these differences may cause helium to form different trapped gas bubble sizes or size distributions within the pore space. For example, if helium bubbles were smaller and more uniformly dispersed throughout the pore space the effect of trapped gas on the distribution of pore water velocities would be smaller, and no appreciable change in dispersivity would be observed. Also the volume of trapped gas varied greatly during the helium experiments, sometimes changing by as much as 50 % during an experiment and this may have masked the effect of varying pore size distribution due to trapped gas Effect of Trapped Gas on R Estimated values of the retardation factor for dissolved oxygen, R, increased with increasing volume of trapped gas (Table 2.2). Example dissolved oxygen breakthrough curves for experiments 2 and 3 illustrate this trend (Figure 2.5b). Dissolved oxygen concentrations in the column effluent reached the feed concentration more quickly in experiment 2, where R = 3.28, than in experiment 3, where R = The solid lines through the data represent the fits from the kinetic model and illustrate the ability of the model to predict the experimental curves. This observed variation in retardation factor with trapped gas content was supported by the results of other experiments (Table 2.2); in general estimated values of R increased approximately linearly with increasing 0g/0aq (Figure 2.6b).

41 O 30 O O O co cv oo d Figure 2.6. Effect of trapped gas volume on fitted values of (a) Peclet number, P (b) retardation factor, R, and (c) dimensionless parameter, co. Dashed line in (b) is computed using equation 1 with H = 28 for dissolved oxygen at 15 C.